Astronomy Principles and Practice Fourth Edition.pdf

14.6 Dynamics of artificial Earth satellites
14.6.1 Forces acting on artificial satellites
Dynamics of artificial Earth satellites 193
Since October 4th, 1957, many hundreds of artificial satellites have been placed in orbit about the Earth.
We have seen (section 13.3) that Newton himself showed that if the projectile was given a sufficient
velocity outside the Earth’s atmosphere, it would become a satellite of the Earth. But it was only by
the development of the rocket during and after the Second World War that a means was provided of
imparting to a payload of instruments the velocity necessary to keep it in orbit.
Artificial satellites are subject to Newton’s laws of motion and the law of gravitation. They
usually obey Kepler’s laws very closely. If the Earth were a point-mass and no other force acted
upon the satellite, a satellite would obey Kepler’s laws exactly and remain in orbit for ever. Many
forces, however, may act on the satellite. Among these forces are:
(1) the Earth’s gravitational field,
(2) the gravitational fields of the Sun, Moon and the planets,
(3) the Earth’s atmosphere and
(4) the Sun’s radiation pressure.
In almost every case, the orbital changes produced by the Sun, Moon and the planets are so small
that they can be neglected. Only in the case of those artificial satellite orbits that take the satellite
many thousands of kilometres away from the Earth does the disturbing effect of the Moon have to be
considered. Even then, it is still small.
As a result of the momentum associated with photons within any flow of radiation, the flux
produces a pressure or force on any surface which intercepts the radiation (see section 13.7). For
a satellite whose size is large (for example a balloon satellite) and whose mass is small, the Sun’s
radiation pressure can produce large changes in the satellite orbit over many months. For all other
satellites, the orbital changes due to solar radiation pressure are negligible unless orbital positions are
required to very high precision.
The two main causes of change in a satellite orbit are, therefore, the departure of the Earth’s shape
from that of a perfect sphere and the drag due to the Earth’s atmosphere on those satellites low enough
to experience it. We examine each in turn.
14.6.2 Effect of the Earth’s shape on a satellite orbit
The Earth is not a perfect sphere. Even before the days of artificial satellites, it was known that the
diameter of the Earth, measured from pole to pole, was about 43 km less than an equatorial diameter.
Newton explained this equatorial bulge of matter as being a consequence of the Earth’s rapid rotation.
The departure of the Earth from a sphere, therefore, acts gravitationally as a disturbing force on the
satellite. Indeed, it acts upon the Moon itself, producing perturbations in its orbit.
Many artificial satellites are so close to the Earth that other departures of the Earth’s shape from a
sphere produce observable changes in the satellite orbits. By predicting the types of orbital change due
to particular departures and then observing them, our knowledge of the Earth’s figure, asitiscalled,
has increased enormously. For example, the equator is found to be elliptical rather than circular, the
difference between longest and shortest equatorial diameters being about half a kilometre. The northern
hemisphere is slightly sharper than the southern hemisphere, imparting a ‘pear-shaped’ aspect to our
planet. The order of magnitude of this difference is only about 20 m. Other, even smaller, features of
the Earth’s figure have been measured.
The effects upon a satellite orbit due to these causes are best described by the changes that take
place in the orbital elements. The semi-major axis, eccentricity and inclination of the orbital plane
suffer purely periodic changes. This means that the Earth’s departure from a sphere has no disastrous